diff --git a/base/special/log/README.md b/base/special/log/README.md
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--- a/base/special/log/README.md
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@license Apache-2.0
-Copyright (c) 2018 The Stdlib Authors.
+Copyright (c) 2024 The Stdlib Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
@@ -85,6 +85,96 @@ for ( i = 0; i < 100; i++ ) {
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+* * *
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+## C APIs
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+### Usage
+
+```c
+#include "stdlib/math/base/special/log.h"
+```
+
+#### stdlib_base_log( x, b )
+
+Computes the base `b` logarithm of `x`.
+
+```c
+double v = stdlib_base_log( 100.0, 10.0 );
+// returns 2.0
+```
+
+The function accepts the following arguments:
+
+- **x**: `[in] double` input value.
+- **b**: `[in] double` input value.
+
+```c
+double stdlib_base_log( const double x, const double b );
+```
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+### Examples
+
+```c
+#include "stdlib/math/base/special/log.h"
+#include
+#include
+
+int main( void ) {
+ double out;
+ double x;
+ double b;
+ int i;
+
+ for ( i = 0; i < 100; i++ ) {
+ x = ( (double)rand() / (double)RAND_MAX ) * 100.0;
+ b = ( (double)rand() / (double)RAND_MAX ) * 5.0;
+ out = stdlib_base_log( x, b );
+ printf( "log(%lf, %lf) = %lf\n", x, b, out );
+ }
+}
+```
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